Examples of torsion points on genus two curves
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- by John Boxall and David Grant PDF
- Trans. Amer. Math. Soc. 352 (2000), 4533-4555 Request permission
Abstract:
We describe a method that sometimes determines all the torsion points lying on a curve of genus two defined over a number field and embedded in its Jacobian using a Weierstrass point as base point. We then apply this to the examples $y^{2}=x^{5}+x$, $y^{2}=x^{5}+5 x^{3}+x$, and $y^{2}-y=x^{5}$.References
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Additional Information
- John Boxall
- Affiliation: CNRS, UPRESA 6081, Département de Mathématiques et de Mécanique, Université de Caen, Boulevard maréchal Juin, B.P. 5186, 14032 Caen cedex, France
- Email: boxall@math.unicaen.fr
- David Grant
- Affiliation: Department of Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309-0395
- Email: grant@boulder.colorado.edu
- Received by editor(s): October 6, 1997
- Received by editor(s) in revised form: April 18, 1998
- Published electronically: June 8, 2000
- Additional Notes: The first author was enjoying the hospitality of the University of Colorado at Boulder while the paper was completed. The second author was supported by NSF DMS–930322 and was enjoying the hospitality of the University of Caen while conducting part of this research
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 4533-4555
- MSC (2000): Primary 11G30, 14H25
- DOI: https://doi.org/10.1090/S0002-9947-00-02368-0
- MathSciNet review: 1621721